Retroreflection device

ABSTRACT

The first reflective lateral face of the first triangular-pyramidal retroreflective unit is on the same plane with the first lateral face of the tetrahedral retroreflective unit, the second reflective lateral face of the first triangular-pyramidal retroreflective unit is on the same plane with the second lateral face of the tetrahedral retroreflective unit, the third reflective lateral face of the first triangular-pyramidal retroreflective unit is parallel to one of the two lateral faces forming a V-shaped groove, the third reflective lateral face of the second triangular-pyramidal retroreflective unit is identical with, or parallel to, the other of the two faces forming said V-shaped groove, and the third reflective lateral face of said tetrahedral retroreflective unit is same as one of the two faces forming said V-shaped groove.

TECHNICAL FIELD TO WHICH THE INVENTION BELONGS

This invention relates to a triangular-pyramidal cube-cornerretroreflective sheeting and retroreflective articles of novelstructures. More particularly, the invention relates to aretroreflective device in which a large number of complex cube-cornerretroreflective elements are arranged in closest-packed state, each ofsaid complex cube-corner retroreflective elements having a first andsecond triangular-pyramidal retroreflective units and at least onetetrahedral retroreflective unit.

Specifically, the invention relates to a retroreflective device in whicha large number of complex cube-corner retroreflective elements arearranged in closest-packed state, each of said complex cube-cornerretroreflective elements having a first and second triangular-pyramidalretroreflective units and at least one tetrahedral retroreflective unit,which device is useful for signs such as traffic signs (commonly usedtraffic signs and delineators), road surface signs (pavement markers)and construction signs; number plates for vehicles such as automobilesand motorcycles; safety goods such as reflective tapes to be adhered tobodies of tracks or trailers, clothing and life preservers; marking onsignboards; and reflective plates of visible light, laser-beams orinfrared light-reflective sensors.

That is, the invention relates to a retroreflective device in which alarge number of complex cube-corner retroreflective elements arearranged in closest-packed state, each of said complex cube-cornerretroreflective elements having a first and second triangular-pyramidalretroreflective units and at least one tetrahedral retroreflective unit,characterized in that the three reflective lateral faces (a1, b1, c1 anda2, b2, c2) of each of the first and second triangular-pyramidalretroreflective units form mutually perpendicular cube-corner reflectivesurfaces, respectively, the first reflective lateral face (f1) of saidat least one tetrahedral retroreflective unit, the second reflectivelateral face (e1) and the third reflective lateral face (g1) thereofform a mutually perpendicular cube-corner reflective surfaces,

-   -   said first reflective lateral face (a1) of the first        triangular-pyramidal retroreflective unit is on the same plane        with the first lateral face (f1) of said tetrahedral        retroreflective unit,    -   said second reflective lateral face (b1) of the first        triangular-pyramidal retroreflective unit is on the same plane        with the second lateral face (e1) of said tetrahedral        retroreflective unit,    -   said complex cube-corner retroreflective element has a        quadrangular circumference defined by mutually parallel y-lines        and mutually parallel z-lines,    -   said complex cube-corner retroreflective element has a        substantially symmetrical V-shaped groove with its center line        x-x′ passing through the points of intersection of said parallel        y-lines and parallel z-lines,    -   the third reflective lateral face (c1) of said first        triangular-pyramidal retroreflective unit is parallel to one of        the two lateral faces (g1) forming said V-shaped groove,    -   the third reflective lateral face (c2) of said second        triangular-pyramidal retroreflective unit is parallel to the        other (g2 or c2) of the two faces forming said V-shaped groove,        and    -   the third reflective lateral face (g1) of said tetrahedral        retroreflective unit is same as one of the two faces forming        said V-shaped groove.

PRIOR ART

Retroreflective sheetings and retoreflective articles which reflectincoming light rays toward the light sources are well known, and suchsheetings whose retroreflectivity is utilized are widely used in thefields as above-described. Of those, particularly cube-cornerretroreflective sheetings and retroreflective articles which utilize theretroreflection principle of cube-corner retroreflective elements suchas triangular-pyramidal reflective elements exhibit drastically higherretroreflectivity of light compared with those of conventional microglass bead retroreflective sheetings or retroreflective articles, anddue to the excellent retroreflective performance their utility is yearlyincreasing.

Whereas, heretofore known triangular-pyramidal retroreflective elementexhibits favorable retroreflectivity where an angle formed by itsoptical axis (an axis passing through the apex of the triangular-pyramidand the point equidistant from the three faces which intersect with eachother at an angle of 90° and constitute the triangular-pyramidalcube-corner retroreflective element) with an entering light (which angleis hereafter referred to as an entrance angle) is small. However,because of its principle of reflection, retroreflectivity of the elementrapidly decreases as the entrance angle broadens (i.e., entranceangularity is inferior).

Furthermore, a light ray from a light source which enters into such atriangular-pyramidal reflective element surface at an angle less thanthe critical angle (αc) satisfying the total internal reflectioncondition, which is determined by the ratio of the refractive index ofindividual transparent medium constituting said triangular-pyramidalreflective element and the refractive index of ambient air, is nottotally reflected at the interfaces of the element but is transmitted tothe back of the element. Hence retroreflective sheetings and articlesusing triangular pyramidal reflective elements have a defect that theyare generally inferior in entrance angularity.

On the other hand, because a triangular pyramidal retroreflectiveelement can reflect a light ray toward the incoming direction of thesame ray from over nearly the whole area of the element, the reflectedlight is not excessively diverged for such causes as sphericalaberration, unlike micro glass bead reflective elements.

From practical standpoint, however, the narrow divergence angle ofretroreflective light is apt to produce such an inconvenience, e.g.,when light rays emitted from head lamps of a car are retroreflected by atraffic sign, the reflected light rays are difficult to be caught by thedriver of the car at a position deviating from the incidental axis ofthe light. This kind of inconvenience is enhanced particularly as thecar approaches near the traffic sign, because the angle (observationangle) formed by the incidental axis of the light and the axis(observation axis) connecting the driver and the point of reflectionincreases (i.e., observation angurality becomes inferior).

For improving entrance angurality or observation angurality ofcube-corner retroreflective sheetings and retroreflective articles, inparticular, triangular-pyramidal cube-corner retroreflective sheetingsand retroreflective articles, many proposals have been made of old andvarious improving means have been investigated.

For example, U.S. Pat. No. 2,481,757 to Jungersen describes installationof various forms of retroreflective elements on a thin sheet.Triangular-pyramidal reflective units exemplified in said US Patentinclude those in which their optical axes are not tilted, the positionof their apices corresponding to the center points of their respectivetriangular bases, and tilted triangular-pyramidal reflective units whoseapices do not correspond to the center points of their respectivetriangular bases, and the patent states that the sheeting effectivelyreflects light rays toward an approaching car (improvement in entranceangularity).

As the size of the triangular-pyramidal reflective units, the samepatent states, as the depth of the units, up to one tenth of an inch(2,540 μm). Furthermore, FIG. 15 of this US patent shows atriangular-pyramidal reflective unit pair whose optical axes are tiltedin positive (+) directions as explained later, the angle of tilt (θ) ofeach optical axis being presumed to be approximately 6.5°, as calculatedfrom the length ratio between the longer side and the shorter side ofthe triangular base of the shown triangular-pyramidal reflective unit.

Said US patent to Jungersen, however, contains no specific disclosureabout extremely small size triangular-pyramidal reflective units asdescribed later, or no disclosure or suggestion about the desirable sizeor tilt in optical axis of triangular-pyramidal reflective units forexhibiting excellent observation angularity or entrance angularity.

U.S. Pat. No. 3,712,706 to Stamm discloses a retroreflective sheetingand a retroreflector in which so called regular triangular-pyramidalcube corner retroreflective elements whose triangular bases are in theshape of regular triangles are arranged in the closest-packed state withsaid bases lying on a common plane of a thin sheet. This US patent toStamm specularly reflects incident light by vapor depositing a metalsuch as aluminum on reflective surfaces of the reflective elements, toincrease the incident angle, whereby improving the problem such as thedrop in retroreflective efficiency and such a drawback that an incidentlight entered at an angle less than the total internal reflectioncondition transmits through interfaces of the elements and does notretroreflect.

However, because the above proposal by Stamm provides a specular layeron reflective lateral faces as a means to improve wide angularity, suchdrawbacks as that appearance of the formed retroreflective sheeting andretroreflector is apt to become dark, or the metal used for the specularlayer such as aluminum or silver is oxidized during use by infiltratedwater or air, which leads to occasional decrease in reflectivity.Furthermore, this patent is entirely silent on the means for improvingwide angularity by tilting optical axes.

EP 137,736 B1 to Hoopman describes a retroreflective sheeting andretroreflector in which multitude of pairs of tiltedtriangular-pyramidal cube-corner retroreflective elements having theirbases on a common plane are arranged at the highest density on a thinsheet, each pair of said elements having isosceles triangular bases andbeing rotated 180° from one another. The optical axis of thetriangular-pyramidal retroreflective element as described in this patentis tilted in negative (−) direction in the sense described in thepresent specification, the angle of tilt being about 7°-13°.

U.S. Pat. No 5,138,488 to Szczech also discloses a retroreflective sheetand retroreflective article, in which tilted triangular-pyramidalcube-corner retroreflective elements each having an isosceles triangularbase are arranged on a thin sheet in such a manner that their bases areon a common plane at the highest density. In this US patent, opticalaxes of each two triangular-pyramidal reflective elements, which faceeach other and form a pair, are tilted toward the common edgetherebetween, i.e., in the positive (+) direction as later explained,the angle of tilt being about 2°-5° and the element height being 25 μm-100 μm.

Also in EP 548,280 B1 corresponding to the above patent states that thedirection of tilt in the optical axes is such that the distance betweenthe apex of the element and a plane, which contains the common edge ofsaid pair of elements and is perpendicular to the common base plane, isnot equal to the distance between said plane and the point ofintersection of the optical axis with the common plane, the angle oftilt being about 2°-5° and the element height being 25 μm -100 μm.

As above, EP 548,280 B1 to Szczech proposes an angle of tilt of theoptical axis within a range of about 2°-5°, inclusive of both positive(+) and negative (−) regions. Examples given in said US patent and EPpatent to Szczech, however, disclose only those triangular-pyramidalreflective elements with their optical axes canted with an angle of tiltof (−)8.2°, (−)9.2° or (−)4.3°, having an element height (h) of 87.5 μm.

Those triangular-pyramidal cube-corner retroreflective elements knownfrom so far described U.S. Pat. No 2,481,757 to Jungersen, U.S. Pat. No.3,712,706 to Stamm, EP 137,736 B1 to Hoopman, U.S. Pat. No. 5,138,488and corresponding EP 548,280 B1 to Szczech have the features in common,as illustrated in FIG. 3, that the multitude of triangular-pyramidalreflective elements, which play the kernel role in receiving enteringlight and reflecting the same, have their bases positioned in a commonplane and that each of matched pairs facing with each other have similarconfiguration and equal height. Such retroreflective sheets and articlesconstructed of triangular-pyramidal reflective elements with their basespositioned in a common plane are invariably inferior in entranceangularity, i.e., they are subject to a defect that retroreflectivityrapidly drops with increased entrance angle of light rays entering intothe triangular-pyramidal reflective elements.

Furthermore, retroreflective element arrays including asymmetricalretroreflective element pairs, V-shaped grooves extending in threedirections not intersecting at any one point are also known.

U.S. Pat. Nos. 5,831,767 and 5,557,836 to Benson, et al. discloseretroreflective articles and methods of preparation thereof, which areproposed for the purpose of improving retroreflective efficiency andwide angurality, said articles being constructed of retroreflectiveelement arrays bounded by asymmetric V-shaped grooves in which one ofthe side walls has an angle approximately perpendicular or close theretowith the base plane.

In these Benson, et al.'s retroreflectors, as shown in saidinternational publications, a substrate is so machined that two sets oftilted V-shaped grooves of different directions form rhombic bases andanother set of tilted V-shaped grooves of still different direction arecut not to pass any point of intersection of said rhombic base pattern.By varying the crossing angle, depth, angle of V-shape and degree oftilt in the V-shape each of the first and second sets of groovesextending in two different directions; and the off-set position, numberof grooves, depth, angle of V-shape and extent of tilt in the V-shape ofthe third set of grooves of a still different direction, large varietiesof reflecting elements including those not exhibiting retroreflectivitycan be formed, which constitute the retroreflector.

Furthermore, it is clearly indicated: because one side wall surface ofeach V-shaped groove in the retroreflective article of Benson, et al. isapproximately perpendicular to the base plane to form an asymmetricalV-shaped groove, the intermediate configuration of the elements havingthe rhombic bases as defined by said V-shaped grooves extending in twodifferent directions is bilaterally asymmetrical as shown in FIG. 2attached to this specification, and at that intermediate stage thereflective lateral surfaces are a2 and b2 in said FIG. 2. Whereas, theintermediate shape in conventional art is formed by symmetrical V-shapedgrooves as shown in FIG. 1, and the reflective lateral surfaces formedare symmetrical, paired surfaces (a1, b1, and a2, b2). Hence thosereflective elements of conventional art formed via the FIG. 1 stagebecome a pair of symmetrical triangular-pyramidal cube-corner elementpair facing with each other as illustrated in FIG. 3 when a pair ofsurfaces (a1, b1 and a2, b2) are cut off with the third V-shaped groove.By contrast, cube-corner elements in Benson, et al.'s retroreflectivearticle, which are formed as plural V-shaped grooves are cut, do notform any pair, as illustrated in FIG. 4. FIG. 6 shows an example of theretroreflective element array as shown in FIG. 30 of Benson, et al.'sU.S. Pat. No 5,831,767.

In such a reflective element array, optical axes of any two reflectiveelements facing with each other across a V-shaped groove are alined inidentical direction, as understood from their configuration. Forexample, where the optical axes are tilted, they are tilted in a samedirection. Consequently, although a certain extent of improvement inobservation angularity can be expected due to divergence of reflectivelight attributable to versatility of the reflective elements, in respectof entrance angularity the reflective element array has very highdirectivity. That is, in the direction to which their optical axes aretilted, excellent entrance angularity can be expected, but the arraymust have inferior entrance angularity in other directions.

U.S. Pat. No. 5,889,615 to Dreyer, et al. shows retroreflective elementpair having plural optical axes constituted of a pair of atriangular-pyramidal cube-corner element and a tent-type cube-cornerelement, which is formed of a pair of triangular-pyramidal cube-cornerreflective elements having one base edge in common and confronting witheach other, with their apices cut off with another V-shaped grooveextending in parallel with said common base edge. FIG. 5 attached to thepresent specification shows four sets of said retroreflective elementpairs arranged in the closest-packed state.

This retroreflective element of Dreyer, et al. has plural optical axeswhich turn to mutually different directions. Hence, light rays comingfrom the directions corresponding to those of optical axes of particularretroreflective elements are effectively reflected by the particularelements, but other elements show markedly decreased reflectionefficiency, and as a whole the retroreflective article has to showinferior retroreflective characteristics.

U.S. Pat. No. 4,775,219 to Appeldorn, et al. discloses a retroreflectivearticle which carries on one surface an array of cube-cornerretroreflective elements, the three lateral reflecting faces of theelements being formed by three intersecting sets of V-shaped grooves, atleast one of the sets including, in a repeating pattern, at least twogroove side angles that differ from one another, whereby the array ofcube-corner retroreflective elements is divided into repeatingsub-arrays that each comprise a plurality of cube-corner retroreflectiveelements in a plurality of distinctive shapes that retroreflect incidentlight in distinctively shaped light patterns.

The retroreflective sheeting obtained according to the above proposal byAppeldorn, et al. shows improved observation angularity to a certainextent, but is insufficient as to improvement in entrance angularity.

U.S. Pat. No. 5,764,413 to Smith, et al. discloses a tiled cube-cornerretroreflective sheeting comprising a substrate having a base surfaceand a structured surface displaced from the base surface, the structuredsurface including at least two distinct arrays of cube corner elements,wherein: each cube corner array is formed by three intersecting sets ofsubstantially parallel grooves including a primary groove set and twosecondary groove sets, for at least one cube corner array, the secondarygroove sets intersect each other to define an included angle less than60°; and a major portion of substantially every groove in the primarygroove set of the at least one cube corner array is disposed in a planethat intersects the edge of the sheeting at an acute angle selected fromthe group of angles consisting of 5 to 25°, 35 to 55°, and 65 to 85°.

U.S. Pat. No. 5,812,315 discloses a retroreflective cube corner articleformed from a substantially optically transparent material, comprising:a substrate having a base surface disposed in a base plane; a structuredsurface displaced from the base surface and including an array of cantedcube corner element matched pairs formed by three mutually intersectingsets of substantially parallel grooves, each matched pair including afirst cube corner element and an optically opposing second cube cornerelement, wherein: a plurality of cube corner elements in the array havetheir symmetry axes canted in a first plane through a cant anglemeasuring between 4° and 15°; the article exhibits its broadest range ofentrance angularity in a second plane, angularly displaced from thefirst plane; and the cube corner elements are oriented such that thesecond plane intersects an edge of the article at an angle less than15°.

Furthermore, U.S. Pat. Nos. 5,822,121 and 5,926,314 disclose cube-cornerarticles wherein a plurality of cube corner elements in the array asabove-described comprise a base triangle bounded by one groove from eachof the three intersecting, groove sets, the base triangle being scalene.

While these proposals by Smith, et al. can achieve improvement inentrance angularity by specifying the angle of the products with theouter edge of the sheeting or by providing at least two arrays, theproducts have a defect that reduction in frontal reflectivity is notablewith the retroreflective elements with heavily canted optical axes.

PROBLEM TO BE SOLVED BY THE INVENTION

Generally as the basic optical characteristics desirable fortriangular-pyramidal retroreflective sheeting and retroreflectivearticle, high reflectivity, i.e., high level (magnitude) of reflectivityrepresented by the reflectivity of light entering from the front of thesheeting, and wide angularity are required. Moreover, concerning thewide angularity, three properties, i.e., observation angularity,entrance angularity and rotation angularity, are required. Of thesethree properties, improvement in entrance angularity is known to beaccomplished by tilting optical axes of retroreflective elements, i.e.,entrance angularity in the direction of tilt of the optical axes isimproved. Whereas, excessive tilt in optical axes increases the arealratio among the reflective lateral faces constituting each element,which leads to reduction in retroreflective efficiency toward lightsource via trihedral reflection, presenting a technical problem.

MEANS TO SOLVE THE PROBLEM

I now have discovered that entrance angularity could be markedlyimproved by a retroreflective device in which a large number of complexcube-corner retroreflective elements are arranged in closest-packedstate, each of said complex cube-corner retroreflective elements havinga first and second trianglar-pyramidal retroreflective units and atleast one tetrahedral retroreflective unit, characterized in that thethree reflective lateral faces (a1, b1, c1 and a2, b2, c2) of each ofthe first and second triangular-pyramidal retroreflective units formmutually perpendicular cube-corner reflective surfaces, respectively,

-   -   the first reflective lateral face (f1), the second reflective        lateral face (e1) and the third reflective lateral face (g1) of        said at least one tetrahedral retroreflective unit form a        mutually perpendicular cube-corner reflective surfaces,    -   said first reflective lateral face (a1) of the first        triangular-pyramidal retroreflective unit is on the same plane        with the first lateral face (f1) of said tetrahedral        retroreflective unit,    -   said second reflective lateral face (b1) of the first        triangular-pyramidal retroreflective unit is on the same plane        with the second lateral face (e1) of said tetrahedral        retroreflective unit,    -   said complex cube-corner retroreflective element has a        quadrangular circumference defined by mutually parallel y-lines        and mutually parallel z-lines,    -   said complex cube-corner retroreflective element has a        substantially symmetrical V-shaped groove with its center line        x-x′ passing through the points of intersection of said parallel        y-lines and parallel z-lines,    -   the third reflective lateral face (c1) of said first        triangular-pyramidal retroreflective unit is parallel to one of        the two lateral faces (g1) forming said V-shaped groove,    -   the third reflective lateral face (c2) of said second        triangular-pyramidal retroreflective unit is parallel to the        other (g2 or c2) of the two faces forming said V-shaped groove,        and    -   the third reflective lateral face (g1) of said tetrahedral        retroreflective unit is same as one of the two faces forming        said V-shaped groove.

BRIEF EXPLANATION OF DRAWINGS

FIG. 1 shows a plan view and cross-sectional view illustrating cuttingprocedure of a retroreflective element pair by a conventionaltechnology.

FIG. 2 shows a plan view and cross-sectional view illustrating cuttingprocedure of a retroreflective element pair by a conventionaltechnology.

FIG. 3 shows a plan view and cross-sectional view of a retroreflectiveelement pair according to a conventional technology.

FIG. 4 shows a plan view and cross-sectional view of a retroreflectiveelement pair according to a conventional technology.

FIG. 5 is a plan view of a retroreflective device according to aconventional technology.

FIG. 6 is a plan view of a retroreflective device according to aconventional technology.

FIG. 7 shows a plan view and cross-sectional view of a retroreflectiveelement pair according to a conventional technology.

FIG. 8 is a graph showing the relationship of angle of tilt in opticalaxis versus retroreflection efficiency.

FIG. 9 shows a plan view and cross-sectional view of a retroreflectivedevice according to the present invention.

FIG. 10 shows a plan view and cross-sectional view of a complexcube-corner retroreflective element according to the present invention.

FIG. 11 shows a plan view and cross-sectional view of a complexcube-corner retroreflective element according to the present invention.

FIG. 12 shows a plan view and cross-sectional view of a complexcube-corner retroreflective element according to the present invention.

FIG. 13 shows a plan view and cross-sectional view of a complexcube-corner retroreflective element according to the present invention.

FIG. 14 is a plan view of a retroreflective device according to thepresent invention.

FIG. 15 is a plan view of a retroreflective device according to thepresent invention.

FIG. 16 is a plan view of a retroreflective device according to thepresent invention.

FIG. 17 is a plan view of a retroreflective device according to thepresent invention.

FIG. 18 shows cross-sectional construction of a retroreflective deviceof the present invention.

FIG. 19 shows cross-sectional construction of a retroreflective deviceof the present invention.

WORKING EMBODIMENTS OF THE INVENTION

Before explaining the present invention, known prior art technologiesare explained.

FIGS. 7(A) and 7(B) are a plan view and cross-sectional view forexplaining a triangular-pyramidal cube-corner retroreflective elementaccording to conventional technology, for comparison with a complexcube-corner retroreflective element of the present invention (which maybe hereafter referred to simply as a complex reflective element).

FIG. 7(A) shows a triangular-pyramidal cube-corner retroreflectiveelement device projecting on a common plane with their bases arranged inthe closest-packed state on said common plane (S-S′) as multiple elementpairs each having one base line (x,x . . ) in common and facing witheach other approximately symmetrically at equal height with respect to aplane (Lx-Lx′) perpendi cular to a common plane (S-S′) including saidcommon base lines (x,x . . . ) of said many elements.

FIG. 7(B) shows the cross-section of said pair of reflective elementsamong the triangular-pyramidal reflective element group shown in FIG.7(A). The element pair consists of canted triangular-pyramidalcube-corner retroreflective elements whose optical axes are tilted inthe directions exactly opposite to each other, the optical axes tiltingtoward said perpendicular plane (Lx-Lx′), i.e., in such directions thatthe respective differences between the respective distances (p1, p2)from the points of intersection (P1, P2) of perpendicular lines drawnfrom apices (H1, H2) of the pair of elements toward the base plane(S-S′) with said base plane (S-S′) to the base line (x,x . . . ) sharedin common by said pair of elements, and the respective distances (q1,q2) from the points of intersection (Q1, Q2) of the optical axes withsaid base plane (S-S′) to said base line (x,x . . . ) shared in commonby the element pair, i.e., (q1-p1, q2-p2), take positive (+) values.Each of these element pairs share a base line (x) in common and faceeach other in the optically similar shapes as rotated 180° from oneanother. The two triangular-pyramidal reflective elements have equalheight (h1, h2).

With increased tilt in the optical axis of above triangular-pyramidalcube-corner reflective element, the areal ratios between one lateralface (c1) of said element to the other lateral faces (a1, b1) alsoincrease. Hence, a retroreflective element whose optical axis isexcessively tilted must have a reduced probability for entering light tobe retroreflected via trihedral reflection and its retroreflectiveefficiency inavoidably drops. The concept is explained referring to FIG.7(A). Within the oval portions (F1, F2) shown in the figure, an incominglight can be effectively retroreflected, while the rest of the portionsmarkedly less contribute to retroreflection. The relevancy of angle oftilt in optical axis with specific coefficient of retroreflection wherethe coefficient of reflection of light entering at an incident angle of5° into a retroreflective element with untilted optical axis is made 1,as determined by the inventor's ray-tracing computer simulation is shownin FIG. 8. The more the optical axis is tilted, the less becomes thespecific coefficient of retroreflection, and it is demonstrated that thespecific coefficient of retroreflection of a retroreflective elementwith its optical axis tilted by 150 drops to about 50% that of theretroreflective element with untilted optical axis.

The invention is explained in further details hereinafter, referring tothe drawings time to time where appropriate.

FIGS. 9(A) and 9(B) show a plan view and cross-sectional view to explainone embodiment of retroreflective element device according to thepresent invention. FIGS. 10(A) and 10(B) show one pair of the complexcube-corner retroreflective elements taken out from the deviceillustrated in FIGS. 9(A) and 9(B).

These figures show a retroreflective device in which many complexcube-corner retroreflective elements, each comprising first and secondtriangular-pyramidal retroreflective units and at least two pairs oftetrahedral retroreflective units, are disposed in the closest-packedstate, said device being characterized in that the three reflectivelateral faces (a1, b1, c1 and a2, b2, c2) of each of the first andsecond triangular-pyramidal retroreflective units form mutuallyperpendicular cube-corner reflective surfaces, respectively, the firstreflective lateral faces (f11, f12 and f21, f22), the second reflectivelateral faces (e11, e12 and e21, e22) and the third reflective lateralfaces (g11, g12 and g21, g22) of said two tetrahedral retroreflectiveunits form mutually perpendicular cube-corner reflective surfaces,respectively,

-   -   said first reflective lateral face (a1) of the first        triangular-pyramidal retroreflective unit is on the same plane        with the first lateral faces (f11 and f12), respectively, of        said tetrahedral retroreflective units,    -   said second reflective lateral face (b1) of the first        triangular-pyramidal retroreflective unit is on the same plane        with the second lateral faces (e11, e12) of said tetrahedral        retroreflective units,    -   said complex cube-corner retroreflective element has a        quadrangular circumference defined by mutually parallel y-lines        and mutually parallel z-lines,    -   said complex cube-corner retroreflective element has a        substantially symmetrical V-shaped groove with its center line        x-x′ passing through the points of intersection of said parallel        y-lines and parallel z-lines,    -   the third reflective lateral face (c1) of said first        triangular-pyramidal retroreflective unit is parallel to one        (g11) of the two lateral faces forming said V-shaped groove,    -   the third reflective lateral face (c2) of said second        triangular-pyramidal retroreflective unit is parallel to the        other (g21) of the two faces forming said V-shaped groove, and    -   the third reflective lateral face (g11) of said tetrahedral        retroreflective unit is same as one of the two faces forming        said V-shaped groove.

Whereby formed three pairs of cube-corner retroreflective units, opticalaxes of each pair having substantially same tilt (θ) in respect of thecommon base line (x) although differing in direction by 180° to eachother, constitute the complex cube-corner retroreflective element.

FIGS. 9(B) and 10(B) show cross-sections of each pair of the complexcube-corner retroreflective elements constituting the retroreflectiveelement device as shown in FIGS. 9(A) and 10(A). The pair of elementsare tilted complex cube-corner retroreflective elements and optical axesof each element forming the pair (t11, t12, t13 and t21, t22, t23,respectively) are tilted in the exactly opposite directions, by an angleθ to a plane (Lx-Lx′) perpendicular to the base plane (S-S′) includingthe common base lines (x,x,x . . . ) in such a direction that thedifference (q11-p11) between the distance (p11) from a point ofintersection (P11) of a perpendicular line drawn from one apex (H11) ofan element of said pair toward the base plane (S-S′) with said baseplane, to the base lines (x,x . . . ) shared in common by the elementpair, and the distance (q11) from the point of intersection (Q11) of theoptical axis passing said apex (H11) with said base plane to the baselines (x,x . . . ) shared in common by the element pair, takes apositive (+) value. In these element pairs, heights of the first andsecond triangular-pyramidal reflective units in the forms rotated by180° to one another in respect of the common base line (x) is the same,as so are the heights of respectively matched tetrahedralretroreflective units.

Because the complex cube-corner retroreflective elements used in theinvention can contain plural optical axes (t11, t12, t13 and t21, t22,t23 in FIG. 10) in one pair, improvement can be achieved in the drawbackarising particularly when tilt in optical axis is increased that theareal ratio of one of reflective lateral face (c1) of an element to theother reflective lateral faces (a1, b1) as shown in FIG. 7(A) becomesgreat and the element's reflective efficiency drops. The fourth V-shapedgroove set (w-lines) can traverse, for example referring to FIG. 7(A),other portions of the lateral faces a1 and b1 not contributing toretroreflection, without treversing the effective retroreflectiveregions (F1, F2). This enables to increase the effective areas of theelement's reflective lateral faces, and hence to improve the drawback ofdrop in retroreflective efficiency with increased degree of tilt of theoptical axis as demonstrated in FIG. 8.

FIGS. 11(A) and (B) illustrate another embodiment of complex cube-cornerretroreflective element.

FIGS. 11(A) and 11(B) concern a retroreflective device in which a largenumber of complex cube-corner retroreflective elements are arranged inclosest-packed state, each of said complex cube-corner retroreflectiveelements having a pair of triangular-pyramidal retroreflective units anda pair of tetrahedral retroreflective units, characterized in that thethree reflective lateral faces (a1, b1, c1 and a2, b2, c2) of each ofthe pair of triangular-pyramidal retroreflective units form mutuallyperpendicular cube-corner reflective surfaces, respectively,

-   -   the first reflective lateral faces (f11, f21), the second        reflective lateral faces (e11, e21) and the third reflective        lateral faces (g11, g21) of said pair of tetrahedral        retroreflective units form a mutually perpendicular cube-corner        reflective surfaces, respectively,    -   said first reflective lateral faces (a1, a2) of the pair of        triangular-pyramidal retroreflective units are on the same plane        with the first lateral faces (f11, f21) of said tetrahedral        retroreflective units,    -   said second reflective lateral faces (b1, b2) of the first        triangular-pyramidal retroreflective units are on the same plane        with the second lateral faces (e11, e21) of said tetrahedral        retroreflective units,    -   said complex cube-corner retroreflective element has a        quadrangular circumference defined by mutually parallel y-lines        and mutually parallel z-lines,    -   said complex cube-corner retroreflective element has a        substantially symmetrical V-shaped groove with its center line        x-x′ passing through the points of intersection of said parallel        y-lines and parallel z-lines,    -   the third reflective lateral face (c1) of said first        triangular-pyramidal retroreflective unit is parallel to one        (g11) of the two lateral faces forming said V-shaped groove,    -   the third reflective lateral face (c2) of said second        triangular-pyramidal retroreflective unit is parallel to the        other (g21) of the two faces forming said V-shaped groove, and    -   the third reflective lateral faces (g11, g21) of said pair of        tetrahedral retroreflective units are same as one of the two        faces forming said V-shaped groove, respectively. Optical axes        (t11, t12 and t21, t22) of this complex reflective element have        a substantially same degree of tilt (θ) in respect of the common        base line (x), although differing in direction by 180° to each        other.

FIG. 11(B) shows a complex reflective element in which, where thedistance from an apex (H) to Sx plane determined by the x-line group isexpressed as hx; the distance to Sy plane defined by the y-line group,as hy; the distance to Sz plane defined by the z-line group, as hz, andthat to Sw plane defined by w-ine group determined by base line of thefourth reflective lateral face of said tetrahedral retroreflective unit(d1 or d2), as hw, hx equals hw, hy equals hz, and the ratio of hx to hyis 1.05-1.5.

In the complex cube-corner retroreflective element according to thepresent invention, as illustrated in FIGS.11(A) and 11(B), the V-shapedgrooves providing the base line (x) and base line (w) are formed deeperthan the other grooves providing the base lines (y,z) so that hx equalshw, hy equals hz and the ratio of hx to hy is 1.05-1.5. Hence, comparedwith such elements in which grooves having an identical depth areformed, areas of reflective lateral faces (g11, g21) and of reflectivelateral faces (c1, c2) can be increased to achieve improvement inreflective efficiency.

Such embodiments with deeper grooves are particularly effective, whenthe optical axes are tilted in such directions, where the point ofintersection of a perpendicular line drawn from apex (H) of thetetrahedral retroreflective unit having one of its base lines on x-x′line with Sx plane as defined by x-x′ line group is represented by P andthe point of intersection of the optical axis of same tetrahedralretroreflective unit with said Sx plane is represented by Q, thedifference (q-p) between the distance (q) from x-x′ line to point Q andthe distance (p) from x-x′ line to point P takes a positive (+) value(positive tilting).

It is preferred to deepen the V-shaped grooves formed by x-lines orw-lines to render hx greater than hy, so that the depth ratio, hx/hy,should fall within a range of 1.05-1.5, preferably 1.07-1.4.

In such elements wherein the difference (q-p) between the distance (q)from x-x′ line to point Q and the distance (p) from x-x′ line to point Ptakes a negative value, there appears an opposite tendency from thosehaving positively tilted optical axes, that areas of the reflectivelateral faces (g11, g21) and those (c1, c2) become excessively large ascompared with those elements having grooves of an equal depth. Hence theareas of said reflective lateral faces (g11, g21) and reflective lateralfaces (c1, c2) can be decreased by shallowing the V-shaped grooves whichform the base line (x) and/or base line (w).

In such occasions, it is preferred to shallow the V-shaped grooves whichare formed by x-lines and/or w-lines to make hx greater than hy so thatthe depth ratio, hx/hy, in the elements with negatively tilted opticalaxes should fall within a range of 0.67-0.95, preferably 0.71-0.93.

Generally when a light beam passes through a fine aperture, the beam isdiverged with an intensity inversely proportional to the area of saidaperture, due to diffractive effect. The divergence improves visibilityof reflected light to an observer (vehicle driver) present at a distantplace from the light source (head lamp) (improvement in observationangularity).

Explaining the above referring to, for example, a knowntriangular-pyramidal retroreflective element as shown in FIG. 7(A), theaperture through which a light beam passes signifies the facessurrounded by three reflective lateral faces (a1, b1, c1 or a2, b2, c2)of the shown triangular-pyramids, respectively, (bases of the elements,ABC1 and ABC2) whose area varies in proportion to height of the element.Where the element height is small, the aperture area decreases, anddivergence of the reflected light enlarges due to increased diffractioneffect. According to the calculation based on simulation on computer byray-tracing method, with the element height of 50 μm or less, divergenceof the reflected light rapidly increases. On the other hand, excessivelysmall element dimensions results in excessive divergence of light andleads to decrease in retroreflection intensity in the front directionfrom which the light entered.

The complex cube-corner retroreflective element according to the presentinvention includes plural optical axes differing in height, and thecube-corner units each having one optical axis have aperture areadiffering from one another. This enables to enlarge divergence ofreflected light by increased diffractive effect, without excessivelyreducing the element height, which leads to improvement in observationangularity compared with known element pairs containing a pair ofoptical axes.

Where the reflective element height (h) is less than 30 μm, thereflective element size becomes too small, and due to the diffractioneffect which is decided by the aperture area of the reflective element,divergence of retroreflected light becomes excessive to reduceretroreflectivity. Whereas, any of the heights (h) of the elementexceeding 400 μm is undesirable because it renders thickness of thesheeting too large to make a flexible sheeting.

Therefore, where a windable, flexible sheet-formed product is to beobtained according to the present invention, a cube-corner.retroreflective sheeting having triangular-pyramidal reflective units,in which the distance (hx) from the Sx plane determined by the x-linegroup of the many complex cube-corner retroreflective elements to theapex (H1, H2) of one of the complex cube-corner retroreflective elementpair is 30-400 μm, in particular, 50-200 μm, inter alia, 60-120 μm, ispreferred.

FIGS. 12(A) and 12(B) show a retroreflective device as described in anyone of claims 1-11, which is characterized in that the bottoms of atleast one of those substantially symmetrical V-shaped parallel groovegroups (Vx, Vy, Vz and Vw) which are defined by said x-, y-, z- andw-line groups forming the triangular-pyramidal retroreflective units ortetrahedral retroreflective units are formed of a flat surface or acurved quadratic surface.

In FIG. 12(B), the base of at least one of the substantially symmetricalV-shaped parallel groove groups (Vx and Vw) which are defined by the xand w line groups is formed of a flat surface, and the width of the flatportion at the bottom of the V-shape is δ.

The shape of the bottom of said V shape grooves may be flat or a curvedquadratic surface.

In such a complex cube-corner retroreflective element, thecross-sectional shape of the V-shaped groove (Vx) forming the reflectivelateral faces which face each other (g1, g2) and/or the cross sectionalshape of the fourth V-shaped groove group (Vw) which cut off the lateralfaces (a1, b1) is substantially symmetrical trapezoid, the width (δ) ofthe bottom of the grooves being preferably 3-20 μm. Where such complexcube-corner retroreflective element pairs constructed of the V-shapedgrooves having said cross-sectional shapes are used, such aninconvenience occurring when tilt angle of optical axes is large, i.e.,the bottom angles of the V-shaped grooves (Vx and Vw) become too smalland invite insufficient strength of cutting tool or difficulty inparting the shaped resin product from inverted die having said shape,can be improved.

Where the point of intersection of a perpendicular line drawn from theapex (H) of the tetrahedral retroreflective unit having one of its baselines on x-x′ line of a complex cube-corner retroreflective element ofthe present invention, with the Sx plane determined by x-x′ line groupis made P, and the point of intersection of the optical axis of saidtetrahedral retroreflective unit with said Sx plane is made Q, theoptical axis is tilted to such an extent that the distance (q) betweenx-x′ line and said point Q and the distance (p) between x-x′ line andthe point P are not equal. As the reflective lateral faces (a1, a2) ofthe triangular-pyramidal retroreflective units are disposed on the sameplane with the lateral faces (f1, f2) and the reflective lateral faces(c1, c2) are parallel to the faces (g1, g2) forming the V-shaped groove,respectively, tilt angles of the optical axes of the pair oftriangular-pyramidal retroreflective elements are the same.

Preferably, where the point of intersection of a perpendicular linedrawn from an apex (H) of one of the tetrahedral retroreflective unitshaving one of its base lines on x-x′ line with the Sx plane determinedby x-x′ line group is made P, and the point of intersection of theoptical axis of said tetrahedral retroreflective unit with said Sx planeis made Q, the optical axes are tilted in the direction where thedifference between the distance (q) from the x-x′ line to the point Qand the distance (p) from the x-x′ line to the point P, i.e., (q-p),takes a positive (+) value.

In particular, the optical axes are tilted by 0.5-30°, preferably 5-20°,in the direction, where the point of intersection of a perpendicularline drawn from an apex (H) of one of the tetrahedral retroreflectiveunits having one base line on x-x′ line with the Sx plane determined byx-x′ line group is made P, and the point of intersection of the opticalaxis of said tetrahedral retroreflective unit with said Sx plane is madeQ, that the difference between the distance (q) from the x-x′ line tothe point Q and the distance (p) from the x-x′ line to the point P,i.e., (q-p), takes a positive (+) value.

With the view to improve observation angularity a deviation is given, toat least one of the two lateral faces of at least one group of thesubstantially symmetrical V-shaped parallel groove groups (Vx, Vy, Vzand Vw) which are determined by the x-, y-, z- and w-line groups oftriangular-pyramidal retroreflective units or tetrahedralretroreflective unit(s), so that the prism angles of thetriangular-pyramidal retroreflective units or of the tetrahedralretroreflective unit(s) which are formed by said V-shaped parallelgrooves are given a deviation of ±(0.001-0.1)° from 90°.

Furthermore, with the view to impart a uniform observation angularity,it is most advantageous that at least one V-shaped parallel groove groupamong the substantially symmetrical V-shaped parallel groove groups (Vx,Vy, Vz and Vw) which are determined by the x-, y-, z- and w-line groupsof the triangular-pyramidal retroreflective units or tetrahedralretroreflective unit(s), are given deviations such that the verticalangles of the cube-corner reflective elements formed by said group ofV-shaped parallel grooves show deviations of ±(0.001-0.1)° from 90°, ina pattern of repeating at least two different sets of deviations.

As a means to deviate the vertical angles, in the occasion of cuttingthe groove groups in four directions (x, y, z and w) for forming thecomplex cube-corner retroreflective elements, angle of the V-shapedgrooves in at least one direction is minutely and symmetrically deviatedfrom the angle to give 90° to the prism angles. This means to impart thedeviation can be accomplished by using a bilaterally symmetrical cuttingtool.

As another means to impart a deviation to the vertical angles, in theoccasion of cutting the V-shaped grooves in three directions (x, y, zand w) which form the complex cube-corner retroreflective elements, theV-shaped grooves in at least one direction can be cut at an angleminutely and bilaterally asymmetrically deviated from the angle to give90° to the prismatic vertical angles. This means to impart the deviationcan be accomplished by using a bilaterally asymmetrical cutting tool orby slightly canting a bilaterally symmetrical cutting tool at the timeof cutting.

In the V-shaped parallel groove group (Vw) formed symmetrically inrespect of w-lines, the face which forms a right angle with theprismatic vertical angle is only one of the lateral faces or side wallsof the V-shaped groove (referring to FIG. 10, g12, c1 and g22, c2).Therefore, the cross-sectional configuration of the V-shaped groove isnot necessarily symmetrical, but the other side wall not contributing toretroreflection (d12, d11 and d21, d22) can have an optional angle.Whereas, each adjacent complex reflective elements take bilaterallyreversed configurations and cannot form cube-corner reflective faces.Therefore, the V-shaped grooves are preferably substantiallysymmetrical.

Where such retroreflective elements having deviated vertical angles areused, whereby retroreflected light does not return to the light sourcebut retroreflect to a position slightly distant threfrom. Hence thelight can be effectively directed, for example, to a vehicle driver(observer) present at a distant position from the vehicle's head lamps,and the observation angularity is improved. In particular, whereV-shaped grooves are formed with a pattern of repeating at least twosets of deviations to deviate vertical angles of retroreflectiveelements, the retroreflective elements are given various deviations intheir vertical angles to advantageously provide a uniform observationangularity.

FIGS. 13(A) and 13(B) show a complex cube-corner retroreflective elementcomprising a pair of triangular-pyramidal retroreflective units andthree tetrahedral retroreflective units whose bases are difined by baselines in four directions, in which said pair of triangular-pyramidalretroreflective units have different sizes and are disposed at spacedpositions and the three reflective lateral faces (e, f, g) of each ofthe tetrahedral retroreflective units are mutually perpendicular to formcube corners where they meet, said tetrahedral units being disposedbetween the pair of triangular-pyramidal retroreflective units, twobeing at the right side and one, at the left side.

FIG. 14 shows a plan view of a retroreflective device in which a largenumber of the complex cube-corner retroreflective elements as shown inFIG. 13 are disposed in the closest-packed state. FIG. 14 shows arepeated pattern of forming x line group and w line group, in which onew line is formed between two parallel x lines and between the next twoparallel x lines, two w-symmetrical lines are formed.

FIG. 15 shows a plan view of a retroreflective device in which the angleformed between the x lines of the device as illustrated above and anouter edge of a product formed of the retroreflective device is 5-85°,preferably 30-60°. Outer edge of the product as referred to hereinsignifies, where the product is a thin sheet-formed retroreflectivesheeting, the longitudinal edge of a wound-up roll; or, where theproduct is an article like a thick-walled reflector, the edge in thehorizontal direction may be the outer edge; or where the product has acircular shape, the standard edge may be the tangential line in thehorizontal direction.

In such a retroreflective device in which the angle formed between xlines of the retroreflective device and the outer edge of the productformed from the retroreflective device is 5-85°, preferably 30-60°,entrance angularity can be further improved.

FIG. 16 shows a plan view of an example of retroreflective device whichhas first zone(s) and second zone(s), the angle formed between any x1line of the first zone and x2 line in the second zone ranging 5-175°,preferably 80-100°. The two zones are combined in such a manner that theangle [η1] of the first zone formed with the outer edge is 0° and theangle [η2] of the second zone formed with the outer edge is 90°, whichare disposed in repetitive pattern.

FIG. 17 shows a plan view of an example of a retroreflective device inwhich a first zone and second zone are combined in repeated pattern, insuch a manner that the angle [η1] of the first zone formed with theouter edge is 135°, and the angle [η2] of the second zone with the outeredge is 45°.

Such a retroreflective device having first zone(s) and second zone(s),x1 line of the first zone and x2 line of the second zone form an angleof 5-175°, preferably 80-100°, can uniformize entrance angularity inhorizontal and vertical directions and directions therebetween, bycombining said zones.

Furthermore, the retroreflective device may have three or more zones, inwhich x-lines of each zone are selected to form divided angles with theouter edge so that the angles become uniform in all directions. Bycombining the zones in such a manner, entrance angularity in horizontaldirection and perpendicular direction and directions therebetween can bestill more uniformized.

The most favorable retroreflective device according to the presentinvention is a retroreflective device in which many complex cube-cornerretroreflective elements, each comprising first and secondtriangular-pyramidal retroreflective units and at least a pair oftetrahedral retroreflective units, are disposed in the closest-packedstate,

-   -   said device being characterized in that all the tetrahedral        retroreflective units have an identical shape and mutually form        rotation symmetrical pair as rotated by 180° to one another,        said complex cube-corner retroreflective elements have        rotation-symmetrical shapes,    -   where the point of intersection of a perpendicular line drawn        from the apex (H) of the tetrahedral retroreflective unit having        one base line on x-x′ line with Sx plane determined by x-x′ line        group is made P and the point of intersection of the optical        axis of said tetrahedral retroreflective unit with said Sx plane        is made Q, the optical axis is tilted by 5-20° in the direction        such that the difference between the distance (q) from x-x′ line        to the point Q and the distance (p) from x-x′ line to the point        P, i.e., (q-p), takes a positive (+) value,    -   in the tetrahedral retroreflective unit having one of its base        lines on said x-x′ line, hx equals hw, hy equals hz, and the        ratio of hx to hy is 1.05-1.5, and    -   among the substantially symmetrical V-shaped parallel groove        groups (Vx, Vy, Vz and Vw) determined by x-, y-, z- and w-line        groups forming the triangular retroreflective units or the        tetrahedral retroreflective units, at least one bottom is formed        of a flat or quadratic bottom plane.

In general, triangular-pyramidal cube-corner retroreflective sheetingsand retroreflective articles of the present invention can bemanufactured with cube-corner-molding dies, e.g., a metallic belt onwhich reversed female pattern of complex cube-corner retroreflectiveelements are arranged in closest-packed state as described in theforegoing is inscribed. By hot-pressing a pliable, adequate resin sheetexcelling in optical transparency and uniformity as described lateragainst such a molding die, the pattern inscribed on the die istransferred to the resin in reversed form, to provide a desired product.

A representative method for manufacturing above cube-corner molding dieis described in detail, for example, in earlier cited U.S. Pat. No3,712,706 to Stamm. A method analogous to said method can be adoptedalso in this invention.

Specific exlanation is given referring to the triangular-pyramidalcube-corner elements as illustrated in FIGS. 9 (A) to 13. On a substratewith a flatly ground surface, V-shaped parallel groove groups in twodirections (e.g., in the directions of y lines and z lines in FIG.9(A)), the groove groups having an identical depth (hy or hz) andsubstantially symmetrical cross-sectional shape, are cut, the repetitionpitch in each direction, groove depth (e.g., h in FIG. 9(B), and mutualcrossing angle of said grooves being determined according to theconfiguration of desired triangular-pyramidal reflective elements, witha super-hard cutting tool (e.g., diamond-tipped tool or tool made oftungsten carbide) having a point angle of around 47-86°.

Then another group of parallel, V-shaped grooves having a same depth(hx) and substantially symmetrical cross-section are so cut in the thirddirection (x-direction) as to pass the intersections (A, B, C1, C2) ofthe previously formed V-shaped grooves in y-direction and z-direction,using a similar super-hard cutting tool having a point angle of about30-110°. Moreover, the fourth group of V-shaped grooves (w-direction)having a depth (hw) are cut in parallel with the V-shaped grooves inx-direction at such a repetition pitch as to divide each pitch betweenany two x grooves into an integral number of plural parts, with asuper-hard cutting tool having a point angle similar to that of the toolused for cutting the V-shaped grooves in x-direction. In the presentinvention, depths of the grooves in x- and w-directions (hx, hw) may bethe same with that of the grooves in y- and z-directions (hy or hz) orcan be made deeper or shallower.

In a preferred embodiment of the present invention, where a windable,flexible sheet-formed product is intended, the V-shaped grooves inx-direction are so cut as to make the distance (h) between the plane(Sx-Sx′ ) inclusive of the many base lines (x,x, . . . ) of the manycomplex cube-corner retroreflective elements projecting on the commonbase (Sx-Sx′ ) and apices (H1, H2) of said complex cube-cornerretroreflective element pair, 30-400 μm, in particular, 50-200 μm, interalia, 60-120 μm. The depth of the V-shaped grooves in y- andz-directions may be same with that of the V-shaped grooves inx-direction, or may be made deeper to give the depth ratio hx/hyz tofall within a range of 1.05-1.5, preferably 1.07-1.4. The depth of theV-shaped grooves in w-direction may be the same to, or different from,that of the grooves in x-direction.

As the substrate suitable for making said microprismatic master mold,metallic materials having a Vickers hardness as defined by JIS Z 2244 ofat least 350, in particular, at least 380, are preferred, specificexamples including amorphous copper, electrodeposited nickel andaluminum; and as alloy materials, copper-zinc alloy (brass),copper-tin-zinc alloy, nickel-cobalt alloy, nickel-zinc alloy andaluminum alloy.

As the substrate, synthetic resins can also be used, which preferablyare those having a glass transition point of at least 150° C, inparticular, at least 200° C, and a Rockwell hardness (JIS Z 2245) of atleast 70, in particular, at least 75, to avoid such inconvenience that aresin softens during the cutting process to make high precision cuttingdifficult. Specific examples of useful resins include polyethylenetetraphthalate resins, polybutylene phthalate resins, polycarbonateresins, polymethyl methacrylate resins, polyimide resins, polyarylateresins, polyether sulfon resins, polyether imide resins and cellulosetriacetate resins.

Thus obtained microprismatic master mold is given an electroformingprocessing to form a metallic coating on its surface. Upon removing themetallic coating from the master mold surface, a metallic die to be usedfor molding a triangular-pyramidal cube-corner retroreflective sheetingor an article of the present invention is provided.

In general, said electroforming is conducted, for example, in 60 wt%aqueous solution of nickel sulfamate, under such conditions as around40° C. and 10A/dm² electric current. As the formation rate ofelectroformed layer, for example, one not faster than about 0.02 mm/hris suitable for providing a uniform electroformed layer. At a formationrate greater than that, troubles such as lack in surface smoothness orformation of defective part in the electroformed layer are apt to becaused.

The first generation electroformed die made from the prismatic mastermold can be repetitively used as an electroformed master die for makingsecond generation electroformed dies. Therefore, plural electroformeddies can be made from one prismatic master mold.

Thus manufactured plural electroformed dies are precisely cut, and canbe assembled and bonded to a final die size for molding microprismaticsheeting of synthetic resin. As a means for the bonding, cut endsurfaces may be simply pressed against each other, or the joining partsof an assembly may be welded by such means as electron beam welding, YAGlaser welding, carbon dioxide gas laser welding, and the like.

The assembled electroformed die is used for molding synthetic resin, asa synthetic resin-molding die. As the means for molding synthetic resin,compression molding or injection molding can be adopted.

Compression molding comprises, for example, inserting a thin-wallednickel electroformed die prepared as above, a synthetic resin sheet of aprescribed thickness and a silicone rubber sheet of approximately 5 mmin thickness as a cushioning material into a compression molding presswhich has been heated to a prescribed temperature; preheating theinserted materials under a pressure of 10-20% that of the prescribedmolding pressure for 30 seconds; and heating and pressurizing saidmaterials under such conditions as around 180-250° C. ad 10-30 kg/cm²,for about 2 minutes. Thereafter the press is cooled to room temperaturewhile maintaining the pressurized condition, and then the pressure isreleased to provide a prismatic molded product.

The injection molding can be conducted using a thick-walledelectroformed nickel die which was formed by the above-described methodas an injection molding die according to accepted practice, and acustomarily used injection molding machine. In that occasion, aninjection molding method wherein a mobile die and fixed die are keptunder pressure during pouring molten resin into the dies, or aninjection compression method can be adopted wherein the mobile die andfixed die are not given a pressure and the molten resin is pouredthrough a minor aperture opened and thereafter the system ispressurized. These methods are suitable particularly for makingthick-walled products, e.g., a pavement marker.

Moreover, about 0.5 mm-thick thin-walled electroformed dies made by theabove method can be bonded by aforementioned welding method to form anendless belt die, which is mounted on a pair of a heating roll and acooling roll and rotated. Onto the belt die on the heating roll, moltensynthetic resin is supplied in sheet form, pressure molded with at leastone silicone roll, cooled on the cooling roll to a temperature nothigher than the glass transition point, and stripped off from the beltdie. Thus a continuous sheet-formed product can be obtained.

Now an embodiment of a structure of preferred cube-cornerretroreflective sheeting and retroreflective article of the presentinvention shall be explained, referring to their cross-sectional viewshown in FIG. 18.

In FIG. 18, the numeral 4 is a reflective element layer in which thecomplex cube-corner retroreflective elements (R1, R2) of the presentinvention are disposed in closest packed state; 3 is a holder layerwhich holds the reflective elements; and the arrow 11 shows thedirection of incident light. Normally the reflective element layer (4)and the holder layer (3) form an integral body (5), but they may be alaminate of two different layers. Depending on the intended use of aretroreflective sheeting or a retroreflective article of the presentinvention and the circumstances under which they are used, a surfaceprotective layer (1), print layer (2) to convey information to a vieweror to impart color to the sheeting, binder layer (7) to provide anairtightly sealed structure to prevent infiltration of water to the backof the reflective element layer, support layer (8) to support the binderlayer (7); and an adhesive layer (9) with a peeling layer (10) foradhering the retroreflective sheeting or the retroreflective article toanother structure, can be provided.

The print layer (2) can be installed normally between the surfaceprotective layer (1) and the holder layer (3) or on the surfaceprotective layer (1) or the reflection surface of the reflectiveelements (4) by such ordinary means as gravure, screen printing, orink-jet printing.

While the material for making said reflective element layer (4) andholder layer (3) is not critical so long as it satisfies pliabilitywhich is one of the objects to be achieved by the present invention, onehaving optical transparency and homogeneity is preferred. Examples ofthe material useful for the invention include polycarbonate resin, vinylchloride resin, (meth)acrylic resin, epoxy resin, polystyrene resin,polyester resin, fluorine-contained resin, polyolefin resin such aspolyethylene resin or polypropylene resin, cellulose resin, andpolyurethane resin. Furthermore, with the view to improveweatherability, ultraviolet absorber, photostabilizer, antioxidant andthe like can be used either singly or in combination. Any of variousorganic pigments, inorganic pigments, fluorescent pigments, dyes,fluorescent dyes as colorlant may also be contained.

For the surface protective layer (1), the same resin as used for theretroreflective element layer (4) can be used, which may be incorporatedwith ultraviolet absorber, photostabilizer, antioxidant and the likewhich can be used either singly or in combination. Still in addition,various organic pigments, inorganic pigments, fluorescent pigments,dyes, fluorescent dyes and the like as colorlant may be incorporated.

It is a general practice with the reflective element layer (4) of thepresent invention, to provide an air layer (6) behind the complexcube-corner retroreflective elements, for enlarging the critical anglesatisfying the total internal reflection conditions. To prevent suchtroubles under conditions of use as decrease in critical angle,.corrosion of metallic layer or the like due to infiltrated moisture, thereflective element layer (4) and the support layer (8) are airtightlysealed by a binder layer (7).

As means for this airtight sealing, those described in U.S. Pat. Nos.3,190,178 and 4,025,159 and JP-Utility Model Show a 50 (1975)-28669A canbe used. As the resin to be used for the binder layer (7), (meth)acrylicresin, polyester resin, alkyd resin, epoxy resin and the like can benamed, and as the bonding means, known thermofusing resin bindingmethod, thermosetting resin binding method, ultraviolet curable resinbinding method, electron beam curable resin binding method and the likecan be suitably adopted.

The binder layer (7) used in the present invention may be applied overthe entire surface of the support layer (8), or can be selectivelyprovided at the bonding portion(s) with the retroreflective elementlayer, by such means as printing method.

Examples of the material for constituting the support layer (8) includeresins for making the retroreflective element layer, film-forming resinsin general, fibers, fabric, metallic foil or plate such as of stainlesssteel or aluminum, which can be used either singly or in combination.

The adhesive layer (9) used for adhering the retroreflective sheeting orretroreflective article of the present invention onto metallic plate,wood board, glass sheet, plastic sheet and the like, and the peelinglayer (10) for the adhesive can be suitably selected from knownmaterials. The adhesive can be suitably selected amongpressure-sensitive adhesives, heat-sensitive adhesives, crosslinkableadhesives and the like. Examples of pressure-sensitive adhesive includepolyacrylate agglutinants obtained by copolymerizing acrylic acid esterssuch as butyl acrylate, 2-ethylhexyl acrylate, isooctyl acrylate, nonylacrylate and the like, with acrylic acid, vinyl acetate and the like;silicone resin agglutinants; and rubber agglutinants. As heat-sensitiveadhesives, acrylic, polyester or epoxy resins can be used.

Now another embodiment of a preferred structure of the cube-cornerretroreflective sheeting or retroreflective article of the presentinvention is explained referring to FIG. 19 which is a cross-sectionalview of the embodiment.

In FIG. 19, a metallic specular reflective layer (12) is provided on thesurfaces of the elements in the reflective element layer (4), and anadhesive layer and a peeling layer are laminated on, and in directcontact with, the specular reflection layer (12). The cube-cornerretroreflective sheeting or retroreflective article of this embodimentdo not require an air layer because they retroreflect on principle ofspecular reflection, and hence do not require any binder layer orsupport layer. The metallic specular reflection layer (12) installed onthe element surfaces in the reflective element layer (4) of the presentinvention may cover the entire region of the element surfaces or coverit only partially.

The specular reflection layer (12) formed of a metal such as aluminum,copper, silver, nickel or the like can be provided on the elements inthe reflective element layer (4) of the triangular-pyramidal cube-cornerretroreflective sheeting or retroreflective article of the presentinvention by such means as vacuum vapor deposition, chemical plating orsputtering. Of these means for providing said specular reflective layer(12), vapor deposition means using aluminum is preferred, because thevapor deposition temperature can be lowered to minimize thermaldeformation of the retroreflective elements during the vapor depositionstep, and also the resulting specular reflective layer (12) shows thefairest color tone.

An apparatus suitable for continuous vapor deposition of aluminumspecular reflection layer (12) comprises a vacuum vessel which iscapable of maintaining a degree of vacuum at around 7 to 9×10⁻⁴ mm Hg,said vacuum vessel accommodating therein a feeder for feeding anoriginal prism sheeting formed of a base sheet and a surface protectivelayer which is laminated on the light entrance side surface of said basesheet; a take-up winder for winding up the original prism sheeting whichhas been vacuum-deposition treated; and a heating system installedtherebetween which is capable of fusing the aluminum in a graphitecrucible with an electric heater. Pure aluminum pellets having a purityof at least 99.99 wt% are put in the graphite crucible, melted andvaporized under the conditions, e.g., an AC voltage of 350-360 V, anelectric current of 115-120 A and a treating rate of 30-70 m/min. Withthe vaporized aluminum atoms, a specular reflection layer (12) can bedeposited on the surfaces of retroreflective elements at a thickness of,for example, 800-2000 Å.

EXAMPLES

Hereinafter the particulars of the present invention are explained morespecifically, referring to working Examples, it being understood thatthe invention is not limited to the Examples only.

<Coefficient of Retroreflection>

Coefficient of retroreflection referred to in the specification, inparticular, in Examples, was measured by the following method. Using areflectometer “Model 920” of Gamma-Scientific Co., coefficients ofretroreflection of each 100 mm×100 mm retroreflective sheeting weremeasured following ASTM E810-91 at optional five spots, under theangular conditions of observation angle, 0.2°; and incident angles, 5°,10°, 20°, 30°, 40° and 500. The mean values of the measured values areindicated as the coefficients of retroreflection of the measuredretroreflective sheeting. Also for comparison of observation angularity,coefficients of retroreflection at an incident angle of 5° andobservation angle of 1.0° were measured.

Example 1

A large number of parallel V-formed groove groups of symmetricalcross-sections were cut in y-direction and z-direction in a repetitivepattern by fly cutting method, on a 100 mm square brass plate with aflatly ground surface, with a diamond-tipped cutting tool having a pointangle of 83.11°. The repetition pitch of V-shaped grooves in y-directionand z-direction was 201.45 μm, the groove depth was 100.00 μm, andcrossing angle of the V-shaped grooves in y-direction with those inz-direction was 38.207°. An intermediate configuration as shown in FIG.1 was formed.

Furthermore, another group of parallel V-shaped grooves were cut in thex-direction in repetitive pattern with a diamond-tipped cutting toolhaving a symmetrical cross-section and point angle of 40.53°, at arepetition pitch of said V-shaped grooves of 307.77 μm and to theV-shaped groove depth of 100.00 μm, each of said grooves passing throughtwo points of intersection of the y-directioned grooves andz-directioned grooves, to form on said brass plate many maletriangular-pyramidal cube-corner elements arranged in closest-packedstate, each element taking an intermediate configuration as illustratedin FIG. 3.

Thereafter still another group of parallel V-shaped grooves were cut ina repetitive pattern in the w-direction with a diamond-tipped cuttingtool having a symmetrical cross-section and a point angle of 40.53°, ata repetition pitch of said V-shaped grooves of 307.77 μm and to theV-shaped groove depth of 100.00 μm, each of said grooves passing throughthe center point of two adjacent V-formed grooves in x-direction. Thuson the brass plate a master mold according to the present invention,formed of a large number of male complex cube-corner retroreflectiveelements which were disposed in the closest-packed state on said plate,was prepared. This master mold was formed of an array of the element asillustrated in FIG. 10 (A), and the number of V-shaped groove inw-direction between two V-shaped grooves in x-direction was one.

In so formed complex cube-corner retroreflective element pair, theheight (h) from the apex (H11 or H21) to the base plane (S-S′) was 100μm. The tilt angle (θ) of each optical axis of this complex cube-cornerretroreflective element was ±15°, and the vertical angles of the threelateral faces constituting the reflective element were invariably 90°.

The cutting parameters used to make the master mold of Example 1 arelisted in the following:

-   -   depth of V-shaped grooves in x-, y-, z- and w-directions: 100.00        μm    -   angle of V-shaped grooves in y- and z-directions: 83.11°    -   angle of V-shaped grooves in x- and w-directions: 40.53°    -   pitch of V-shaped grooves in y- and z-directions: 201.46 μm    -   pitch of V-shaped grooves in x- and w-directions: 307.77 μm    -   crossing angle of y-directioned V grooves with z-directioned V        grooves: 38.21°    -   crossing angle of y- and z-directioned V grooves with        x-directioned V grooves: 70.90°    -   tilt angle of optical axes: 15°

Using this brass master mold, a female cube-corner forming die withreversed configuration made of nickel was prepared by electroformingmethod using a nickel sulfamate solution of 55% in concentration.Compression molding a 200 μm-thick polycarbonate resin sheet (IupilonTMH3000, Mitsubishi Engineering Plastics K.K.) using this molding die,under the conditions of molding temperature of 200° C. and moldingpressure of 50 kg/cm², the resin sheet was cooled to 30° C. under theelevated pressure and removed. Thus a retroreflective device with about150° μm-thick holder layer on whose surface a large number ofpolycarbonate resin complex cube-corner retroreflective elements weredisposed in closest packed state was prepared.

Example 2

A polycarbonate resin retroreflective device in which a large number ofthe complex cube-corner retroreflective elements as illustrated in FIGS.11(A) and 11(B) were disposed in closest-packed state was prepared bythe same method as described in Example 1, except that the depth ofV-shaped grooves in x- and w-directions was made 115.00 μm.

The cutting parameters used to make the master mold of Example 2 arelisted in the following:

-   -   depth of V-shaped grooves in y and z-directions: 100.00 μm    -   depth of V-shaped grooves in x- and w-directions: 115.00 μm    -   angle of V-shaped grooves in y- and z-directions: 83.11°    -   angle of V-shaped grooves in x- and w-directions: 40.53°    -   pitch of V-shaped grooves in y- and z-directions: 201.46 μm    -   pitch of V-shaped grooves in x- and w-directions: 307.77 μm        crossing angle of y-directioned V grooves with z-directioned V        grooves: 38.21°    -   crossing angle of y- and z-directioned V grooves with        x-directioned V grooves: 70.90°    -   tilt angle of optical axes: 15°

Example 3

A polycarbonate resin retroreflective device in which a large number ofthe complex cube-corner retroreflective elements as illustrated in FIG.12(A) and 12(B) were disposed in closest-packed state was prepared bythe same method as described in Example 1, except that the point of thediamond-tipped tool used for cutting V-shaped grooves of x- andw-directions was advancedly lapped to have a width (dw) of 8 μm.

The cutting parameters used to make the master mold of Example 3 arelisted in the following:

-   -   depth of V-shaped grooves in x-, y-, z- and w-directions: 100.00        μm    -   angle of V-shaped grooves in y- and z-directions: 83.11°    -   angle of V-shaped grooves in x- and w-directions: 40.53°    -   pitch of V-shaped grooves in y- and z-directions: 201.46 μm    -   pitch of V-shaped grooves in x- and w-directions: 307.77 μm    -   crossing angle of y-directioned V grooves with z-directioned V        grooves: 38.21°    -   crossing angle of y- and z-directioned V grooves with        x-directioned V grooves: 70.90°    -   width of bottom portion of each of V-shaped grooves in x- and        w-directions: 8 μm    -   tilt angle of optical axes: 15°

Example 4

In the production of the elements according to Example 2, the angles ofdiamond-tipped tools for cutting V-shaped grooves in x- and w-directionswere varied as follows: the angle of tool A was same with that used insaid Example, that of tool B was made asymmetrical by a deviation of±0.01° given to one of the lateral faces forming the V shape, and thatof tool C was made asymmetrical by a deviation of −0.01° given to one ofthe lateral faces forming the V-shape. Using these three kinds ofcutting tools, V-shaped grooves in x- and w-directions were cut in arepetitive pattern of A-B-C, to form a master mold in which a largenumber of complex cube-corner retroreflective elements with varieddeviations given to their vertical angles were disposed inclosest-packed state. Using this master mold a polycarbonate resinretroreflective device in which a large number of complex cube-cornerretroreflective elements were disposed in closest-packed state wasprepared by the method as described in Example 1.

Example 5

A polycarbonate resin retroreflective device in which a large number ofcomplex cube-corner retroreflective elements were disposed inclosest-packed state was prepared from polycarbonate resintriangular-pyramidal cube-corner retroreflective sheet product asprepared in Example 2, in which a large number of complex cube-cornerretroreflective elements were disposed in closest-packed state, saidsheet product being given an azimuth so that the x-lines of saidretroreflective device each formed an angle of 45° with the outer edgethereof.

Example 6

A polycarbonate resin retroreflective device in which a large number ofcomplex cube-corner retroreflective elements were disposed inclosest-packed state was prepared from polycarbonate resintriangular-pyramidal cube-corner retroreflective sheet product asprepared in Example 2, in which a large number of complex cube-cornerretroreflective elements were disposed in closest-packed state, bycombining the sheetings such that two zones, in one of which the x-linesthereof each formed an angle of 45° with the outer edge and in the otherthe x-lines thereof each formed an angle of 135° with the outer edge,should appear repeatedly to form a pattern of 10 mm-wide stripes.

Comparative Example

A polycarbonate resin retroreflective device in which a large number ofcomplex cube-corner retroreflective elements as illustrated in FIG. 3were disposed in closest-packed state was prepared by the same method asin Example 1, except that V-shaped grooves in x-, y- and z-directionswere cut but V-shaped grooves in w-direction were not cut.

The cutting parameters used to make the master mold of the ComparativeExample are listed in the following:

-   -   depth of V-shaped grooves in x-, y- and z-directions: 100.00 μm    -   angle of V-shaped grooves in y- and z-directions: 83.11°    -   angle of V-shaped grooves in x-direction: 40.53°    -   pitch of V-shaped grooves in y- and z-directions: 201.46 μm    -   pitch of V-shaped grooves in x-direction: 307.77 μm    -   crossing angle of y-directioned V grooves with z-directioned V        grooves: 38.21°    -   crossing angle of y- and z-directioned V grooves with        x-directioned V grooves: 70.90°    -   tilt angle of optical axes: 15°

Coefficients of retroreflection of those retroreflective devices asprepared in above Examples 1-6, in which the complex cube-cornerretroreflective elements were disposed in closest-packed state, and thecoefficients of retroreflection of the triangular-pyramidal cube-cornerretroreflective sheeting as prepared in Comparative Example are shown inTable 1. The coefficients of retroreflection of those retroreflectivedevices of Examples 1-6 according to the present invention excelled overthose of the triangular-pyramidal cube-corner retroreflective sheetingof the Comparative Example based on conventional technology, in bothretroreflectivity in the front direction and retroreflectivecharacteristics in directions of large entrance angles.

Furthermore, the observation angularity (observation angle=1.0° ) of theretroreflective device (retroreflective sheeting) in which a largenumber of the complex cube-corner retroreflective elements were arrangedin the closest-packed state, which was prepared from the master mold inwhich a large number of complex cube-corner retroreflective devices withvertical angles deviated in various manner as described in Example 4were arranged in closest-packed state, excelled over observationangularity of other retroreflective devices which were not given suchvertical angle deviations. TABLE 1 Observation Entrance Comparativeangle angle Example 1 Example 2 Example 3 Example 4 Example 5 Example 6Example 0.2° 5° 780 797 631 562 720 704 493 10° 700 747 574 497 704 689470 20° 400 550 374 306 545 544 280 30° 300 362 287 211 420 430 207 40°250 270 216 199 345 350 192 50° 150 169 135 118 321 329 104 1.0° 5° 4543 43 89 39 44 37

1. A retroreflective device in which a large number of complexcube-corner retroreflective elements are arranged in closest-packedstate, each of said complex cube-corner retroreflective elements havinga first and second triangular-pyramidal retroreflective units and atleast one tetrahedral retroreflective unit, characterized in that thethree reflective lateral faces (a1, b1, c1 and a2, b2, c2) of each ofthe first and second triangular-pyramidal retroreflective units formmutually perpendicular cube-corner reflective surfaces, respectively,the first reflective lateral face (f11), the second reflective lateralface (e11) and the third reflective lateral face (g11) of said at leastone tetrahedral retroreflective unit form a mutually perpendicularcube-corner reflective surfaces, said first reflective lateral face (a1)of the first triangular-pyramidal retroreflective unit is on the sameplane with the first lateral face (f11) of said tetrahedralretroreflective unit, said second reflective lateral face (b1) of thefirst triangular-pyramidal retroreflective unit is on the same planewith the second lateral face (e11) of said tetrahedral retroreflectiveunit, said complex cube-corner retroreflective element has aquadrangular circumference defined by mutually parallel y-lines andmutually parallel z-lines, said complex cube-corner retroreflectiveelement has a substantially symmetrical V-shaped groove with its centerline x-x′ passing through the points of intersection of said parallely-lines and parallel z-lines, the third reflective lateral face (c1) ofsaid first triangular-pyramidal retroreflective unit is parallel to oneof the two lateral faces (g11) forming said V-shaped groove, the thirdreflective lateral face (c2) of said second triangular-pyramidalretroreflective unit is identical with, or parallel to, the other (g21)of the two faces forming said V-shaped groove, and the third reflectivelateral face (g11) of said tetrahedral retroreflective unit is same asone of the two faces forming said V-shaped groove.
 2. A retroreflectivedevice according to claim 1, in which all of the tetrahedralretroreflective units form pairs of rotation symmetrical configurationmutually rotated by 180° and said complex cube-corner retroreflectiveelements have a rotation symmetrical configuration.
 3. A retroreflectivedevice according to claim 1, in which at least one tetrahedralretroreflective unit is not in a rotation symmetrical configurationrotated by 180°.
 4. A retroreflective device according to any one ofclaims 1-3, which is characterized in that the optical axis is tilted insuch a manner, where the point of intersection of a perpendicular linedrawn from apex (H) of the tetrahedral retroreflective unit having oneof its base lines on x-x′ line with Sx plane determined by x-x′ linegroup is represented by P and the point of intersection of the opticalaxis of same tetrahedral retroreflective unit with said Sx plane isrepresented by Q, that the distance (q) from x-x′ line to point Q andthe distance (p) from x-x′ line to point P are not the same.
 5. Aretroreflective device according to claim 4, which is characterized inthat the optical axis is tilted in such a manner, where the point ofintersection of a perpendicular line drawn from the apex (H) of thetetrahedral retroreflective unit having one of its base lines on x-x′line with the Sx plane determined by x-x′ line group is represented byP, and the point of intersection of the optical axis of said tetrahedralretroreflective unit with said Sx plane is represented by Q, that thedifference (q-p) between the distance (q) from x-x′ line to point Q, andthe distance (p) from x-x′ line to the point P, takes a positive value.6. A retroreflective device according to claim 5, which is characterizedin that the optical axis is tilted by 0.5°-30° in the direction, wherethe point of intersection of a perpendicular line drawn from an apex (H)of the tetrahedral retroreflective unit having one of its base lines onx-x′ line with the Sx plane determined by x-x′ line group is representedby P, and the point of intersection of the optical axis of saidtetrahedral retroreflective unit with said Sx plane is represented by Q,that the difference between the distance (q) from the x-x′ line to thepoint Q and the distance (p) from the x-x′ line to the point P, i.e.,(q-p), takes a positive (+) value.
 7. A retroreflective device accordingto claim 6, which is characterized in that the optical axis is tilted by5°-20° in the direction, where the point of intersection of aperpendicular line drawn from an apex (H) of the tetrahedralretroreflective unit having one of its base lines on x-x′ line with theSx plane determined by x-x′ line group is represented by P, and thepoint of intersection of the optical axis of said tetrahedralretroreflective unit with said Sx plane is represented by Q, that thedifference between the distance (q) from the x-x′ line to the point Qand the distance (p) from the x-x′ line to the point P, i.e., (q-p),takes a positive (+) value.
 8. A retroreflective device according toclaim 7, which is characterized in, where the distance from an apex (H)of the tetrahedral retroreflective unit to Sx plane determined by thex-line group is expressed as hx; the distance from the same apex to Syplane defined by the y-line group, as hy; the distance to Sz planedefined by the z-line group, as hz, and that to Sw plane defined byw-line group determined by base line of the fourth reflective lateralface (d1 or d2) of said tetrahedral retroreflective unit, as hw, that hxis not equal to at least either one of hy and hz, and hw is not equal toat least either one of hy and hz.
 9. A retroreflective device accordingto claim 8, which is characterized in that hx of the tetrahedralretroreflective unit is greater than at least either one of hy and hz,and hw is greater than at least either one of hy and hz.
 10. Aretroreflective device according to claim 8 or 9, which is characterizedin that the ratio of hx of the tetrahedral retroreflective unit havingone of its base lines on x-x′ line to at least either one of hy and hzis 1.05-1.5, and the ratio of hw to at least either one of hy and hz is1.05-1.5.
 11. A retroreflective device according to claim 10, which ischaracterized in that hx of the tetrahedral retroreflective unit havingone of its base lines on x-x′ line equals hw, hy equals hz, and theratio of hx to hy is 1.05-1.5.
 12. A retroreflective device according toclaim 11, which is characterized in that the bottoms of at least onegroup of those substantially symmetrical V-shaped parallel groove groups(Vx, Vy, Vz and Vw) which are defined by said x-, y-, z- and w-linegroups forming the triangular-pyramidal retroreflective units ortetrahedral retroreflective units, are formed of a flat surface or acurved quadratic surface.
 13. A retroreflective device according claim12, which is characterized in that deviation is given to at least one ofthe two lateral faces of at least one group of the substantiallysymmetrical V-shaped parallel groove groups (Vx, Vy, Vz and Vw) whichare determined by the x-, y-, z- and w-line groups oftriangular-pyramidal retroreflective units or tetrahedralretroreflective unit(s), so that the prismatic vertical angles of thetriangular-pyramidal retroreflective units or of the tetrahedralretroreflective unit(s) which are formed by said V-shaped parallelgrooves are given a deviation of ±(0.00-0.1)° from 90°.
 14. Aretroreflective device according to claim 12, which is characterized inthat deviation is given to at least one V-shaped parallel groove groupamong the substantially symmetrical V-shaped parallel groove groups (Vx,Vy, Vz and Vw) which are determined by the x-, y-, z- and w-line groupsof the triangular-pyramidal retroreflective units or tetrahedralretroreflective unit(s), such that the vertical angles of thecube-corner reflective elements formed by said group of V-shapedparallel grooves show deviations of ±(0.001-0.1)° from 90°, in a patternof repeating at least two different sets of deviations.
 15. Aretroreflective device according to claim 14, in which the angle formedby the x-line of the retroreflective device with an outer edge of aproduct formed of said retroreflective device is 5-85°.
 16. Aretroreflective device according to claim 15, in which the angle formedby the x-line of the retroreflective device with an outer edge of aproduct formed of said retroreflective device is 30-60°.
 17. Aretroreflective device according to claim 16, in which theretroreflective device has a first zone and a second zone, the angleformed by x1-line of said first zone with x2-line of said second zonebeing 5-175°.
 18. A retroreflective device according to claim 17, inwhich the retroreflective device has a first zone and a second zone, theangle formed by x1-line of said first zone with x2-line of said secondzone being 80-100°.
 19. A retroreflective device according to claim 18,which is characterized in that many complex cube-corner retroreflectiveelements, each comprising first and second triangular-pyramidalretroreflective units and at least a pair of tetrahedral retroreflectiveunits, are disposed in the closest-packed state, said device beingcharacterized in that all the tetrahedral retroreflective units have anidentical shape and mutually form rotation symmetrical pair as rotatedby 180° to one another, said complex cube-corner retroreflectiveelements have rotation-symmetrical configurations, where the point ofintersection of a perpendicular line drawn from the apex (H) of thetetrahedral retroreflective unit having one of its base lines on x-x′line with Sx plane determined by x-x′ line group is represented by P andthe point of intersection of the optical axis of said tetrahedralretroreflective unit with said Sx plane is represented by Q, the opticalaxis is tilted by 5-20° in such direction that the difference betweenthe distance (q) from x-x′ line to the point Q and the distance (p) fromx-x′ line to the point P, i.e., (q-p), takes a positive (+) value, inthe tetrahedral retroreflective unit having one of its base lines onsaid x-x′ line, hx equals hw, hy equals hz, and the ratio of hx to hy is1.05-1.5, and among the substantially symmetrical V-shaped parallelgroove groups (Vx, Vy, Vz and Vw) determined by x-, y-, z- and w-linegroups forming the triangular retroreflective units or the tetrahedralretroreflective units, at least one group of said grooves have bottomsformed of flat or quadratic plane.